A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)
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Authors
Mensah Folly-Gbetoula
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
Darlison Nyirenda
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
Abstract
In this paper, we obtain solutions to difference equations of the form
\[ x_{n+1}=\frac{ x_{n-5}}{a_n+b_n x_{n-2}x_{n-5}},\]
where \((a_{n})\) and \((b_{n})\) are sequences of real numbers. Consequently, a result of Elsayed is generalized. To achieve this, we use Lie symmetry analysis.
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ISRP Style
Mensah Folly-Gbetoula, Darlison Nyirenda, A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\), Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 613--623
AMA Style
Folly-Gbetoula Mensah, Nyirenda Darlison, A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\). J. Nonlinear Sci. Appl. (2018); 11(5):613--623
Chicago/Turabian Style
Folly-Gbetoula, Mensah, Nyirenda, Darlison. "A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 613--623
Keywords
- Difference equation
- symmetry
- reduction
- group invariant
MSC
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